LIE COALGEBRAS AND RATIONAL HOMOTOPY THEORY II: HOPF INVARIANTS

Sinha D., Walter B.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.365, sa.2, ss.861-883, 2013 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 365 Sayı: 2
  • Basım Tarihi: 2013
  • Dergi Adı: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.861-883
  • Anahtar Kelimeler: Hopf invariants, Lie coalgebras, rational homotopy theory, graph cohomology
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We develop a new framework which resolves the homotopy periods problem. We start with integer-valued homotopy periods defined explicitly from the classic bar construction. We then work rationally, where we use the Lie coalgebraic bar construction to get a sharp model for Hom(pi*X,Q) for simply connected X. We establish geometric interpretations of these homotopy periods, to go along with the good formal properties coming from the Koszul-Moore duality framework. We give calculations, applications, and relationships with the numerous previous approaches.